How to bake glossy materials?
You can't bake the reflections 100% accurate but you can just hide the object you want to have reflections on and position a panorama camera and make the mesh reflect that panorama. If you do it like that of course you can't see the reflections from the object itself, but you could split your object in parts to achieve complete baked glossy.
In Cycles you could do it like this:


instead of glossy I would then use emission and also mix the color from that environment texture with the diffuse texture